Finite Group Databasebeta

← #30613362

Subgroups — #30613362

Order 15616.

616 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462730C211yesmaximal, characteristic, complemented
2#21462679C211yesmaximal, characteristic
3#21461463C211yesmaximal, characteristic, complemented
4#21461453C211yesmaximal, characteristic, complemented
5#21461446C211yesmaximal, characteristic, complemented
6#21461436C211yesmaximal, characteristic, complemented
7#21461426C211yesmaximal, characteristic, complemented
8#21461424C211yesmaximal, characteristic, complemented
9SD16⋊#92420C211yesmaximal, characteristic, complemented
10SD16×#92420C211yesmaximal, characteristic, complemented
11#21461391C211yesmaximal, characteristic, complemented
12#21461182C211yesmaximal, characteristic, complemented
13#21461119C211yesmaximal, characteristic
14#21461041C211yesmaximal, characteristic, complemented
15#21455826C211yesmaximal, characteristic
16#16840813C2211yescharacteristic, complemented
17#16840813C2211yescharacteristic, complemented
18#16840812—21no—
19#16840811—21no—
20Q8×#92420C2211yescharacteristic, complemented
21Q8×#92420C2211yescharacteristic, complemented
22#16840796C2211yescharacteristic
23#16840796C2211yescharacteristic
24#16840791—21no—
25#16840791—21no—
26D4×#92420C2211yescharacteristic
27D4×#92420C2211yescharacteristic
28#16840787—21no—
29#16840787—21no—
30#16840784C2211yescharacteristic
31#16840781C2211yescharacteristic
32#16840781C2211yescharacteristic
33#16840780C2211yescharacteristic
34#16840733—21no—
35C2×#14519834—21no—
36#16840626C2211yescharacteristic, complemented
37#16840625C2211yescharacteristic, complemented
38#16840624C2211yescharacteristic, complemented
39#16840623C2211yescharacteristic, complemented
40Q8⋊#92420C2211yescharacteristic, complemented
41Q8⋊#92420C2211yescharacteristic, complemented
42Q8⋊#92420C2211yescharacteristic, complemented
43Q8⋊#92420C2211yescharacteristic, complemented
44#16840610C2211yescharacteristic
45#16840610C2211yescharacteristic
46D4⋊#92420C2211yescharacteristic
47D4⋊#92420C2211yescharacteristic
48#92420⋊C8C2211yescharacteristic, complemented
49#92420⋊C8C2211yescharacteristic, complemented
50#16840603C2211yescharacteristic, complemented
51C8×#92420C2211yescharacteristic, complemented
52#16840317C2211yescharacteristic
53C4×D4×D61C2211yescharacteristic
54#16840091C411yescharacteristic
55#16840091C411yescharacteristic
56#16840053C411yescharacteristic
57#16840052C411yescharacteristic
58#16839964C411yescharacteristic
59#16839911C411yescharacteristic
60#16839911C411yescharacteristic
61SD16×Dic61C2211yescharacteristic
62SD16×Dic61C2211yescharacteristic
63#16839847C2211yescharacteristic
64#16839847C2211yescharacteristic
65#16839814C2211yescharacteristic
66C61×#461C411yescharacteristic
67C2×#11758213—21no—
68C2×#11758213—21no—
69C22×#92420—21no—
70C22×#92420—21no—
71#14519844—21no—
72#14519844—21no—
73#14519844—21no—
74C4⋊#92420—21no—
75C4⋊#92420—21no—
76C4⋊#92420D411yescharacteristic
77C4⋊#92420D411yescharacteristic
78C4⋊#92420C2311yescharacteristic
79C4⋊#92420C2311yescharacteristic
80C4⋊#92420C2311yescharacteristic
81C4⋊#92420C2311yescharacteristic
82#14519834—21no—
83#14519834—21no—
84#14519834—21no—
85#14519834—21no—
86#14519834—21no—
87#14519834D411yescharacteristic
88#14519834D411yescharacteristic
89C22⋊#92420—21no—
90C22⋊#92420—21no—
91#14519832—21no—
92#14519832—21no—
93#14519832—21no—
94C4×#92420—21no—
95C4×#92420—21no—
96C4×#92420—21no—
97C4×#92420C2311yescharacteristic
98C4×#92420C2311yescharacteristic
99C4×#92420C2311yescharacteristic
100C4×#92420C2311yescharacteristic
101C2×D4×D61C2×C411yescharacteristic
102C22×C4×D61—21no—
103C2×#11758201C2×C411yescharacteristic
104C2×#11758201C2×C411yescharacteristic
105#14519777C2×C411yescharacteristic
106#14519768—21no—
107#14519757—21no—
108#14519753C2×C411yescharacteristic
109#14519753C2×C411yescharacteristic
110Q8×Dic61C2311yescharacteristic
111Q8×Dic61C2311yescharacteristic
112#14519742—21no—
113C4×D244C2×C411yescharacteristic
114D4×Dic61C2311yescharacteristic
115#14519739C2311yescharacteristic
116C4×C22⋊D61—21no—
117#14519737—21no—
118#14519735—21no—
119C4⋊C4×D61C2×C411yescharacteristic
120C22⋊C4×D61—21no—
121C42×D61C2311yescharacteristic
122#14519709C2×C411yescharacteristic
123#14519709C2×C411yescharacteristic
124#14519708C2×C411yescharacteristic
125#14519708C2×C411yescharacteristic
126C4⋊#92418C2×C411yescharacteristic
127#14519701C2×C411yescharacteristic
128#14519701C2×C411yescharacteristic
129#14519699C2×C411yescharacteristic
130#14519699C2×C411yescharacteristic
131#14519698C2×C411yescharacteristic
132#14519698C2×C411yescharacteristic
133#14519689C2×C411yescharacteristic
134#14519689C2×C411yescharacteristic
135C8×Dic61C2311yescharacteristic
136C8×Dic61C2311yescharacteristic
137C2×SD16×C61C2×C411yescharacteristic
138C2×SD16×C61C2×C411yescharacteristic
139C4⋊Q8×C61C2×C411yescharacteristic
140C4×D4×C61C2×C411yescharacteristic
141C4⋊C8×C61C2×C411yescharacteristic
142#103×C61C2×C411yescharacteristic
143#103×C61C2×C411yescharacteristic
144C23×D61—21no—
145C2×Q8×C61C22×C411yescharacteristic
146C2×Q8×C61C22×C411yescharacteristic
147C2×D4×C61C22×C411yescharacteristic
148C22×C4×C61—21no—
149C2×C22⋊D61—21no—
150C22×Dic61—21no—
151D4×D61—22no—
152D4×D61—41no—
153C2×D244C22×C411yescharacteristic
154C2×C4×D61—21no—
155C2×C4×D61—21no—
156C2×C4×D61—21no—
157C2×C4×D61—81no—
158C2×C4×D61—81no—
159C2×C4×D61C22×C411yescharacteristic
160C2×C4×D61C2×D411yescharacteristic
161C2×C4×D61#4111yescharacteristic
162C2×Dic122—21no—
163C2×#92420—21no—
164C2×#92420—21no—
165C2×#92420—21no—
166C2×#92420—21no—
167C2×#92420—21no—
168C2×#92420—21no—
169C2×#92420—81no—
170C2×#92420—81no—
171C2×#92420C2×D411yescharacteristic
172C2×#92420C2×D411yescharacteristic
173C2×#92420C2×D411yescharacteristic
174C2×#92420C2×D411yescharacteristic
175#11758213—81no—
176#11758213—81no—
177SD16×C61—22no—
178SD16×C61—22no—
179C2×C8×C61C22×C411yescharacteristic
180C2×C8×C61C22×C411yescharacteristic
181C4⋊C4×C61—21no—
182C4⋊C4×C61—21no—
183C4⋊C4×C61C22×C411yescharacteristic
184C22⋊C4×C61—21no—
185C42×C61C22×C411yescharacteristic
186C22⋊Dic61—21no—
187#11758201—41no—
188#11758201—41no—
189#11758198—21no—
190#11758198—21no—
191#11758198—21no—
192#11758198—21no—
193C4⋊Dic61—21no—
194C4⋊Dic61—21no—
195C4⋊Dic61—21no—
196C4⋊Dic61C22×C411yescharacteristic
197C4⋊Dic61C22×C411yescharacteristic
198C4⋊Dic61C22×C411yescharacteristic
199#11758196—21no—
200#11758196—21no—
201#11758196—21no—
202C4×Dic61—21no—
203C4×Dic61—21no—
204C4×Dic61C2×D411yescharacteristic
205C4×Dic61#4111yescharacteristic
206C4×Dic61C2411yescharacteristic
207C2×#92418C22×C411yescharacteristic
208C2×#92418C22×C411yescharacteristic
209C23×C61—21no—
210C22×D61—21no—
211C22×D61—42no—
212C22×D61—42no—
213C22×D61—81no—
214C22×D61C4×D411yescharacteristic
215Q8×C61—21no—
216Q8×C61—21no—
217Q8×C61—21no—
218Q8×C61—21no—
219D4×C61—21no—
220D4×C61#13112yes—
221C2×C4×C61—21no—
222C2×C4×C61—21no—
223C2×C4×C61—21no—
224C2×C4×C61—81no—
225C2×C4×C61C4×D411yescharacteristic
226C2×C4×C61C4×D411yescharacteristic
227C2×C4×C61C23×C411yescharacteristic
228C22⋊D61—42no—
229C2×Dic61—21no—
230C2×Dic61—21no—
231C2×Dic61—21no—
232C2×Dic61—41no—
233C2×Dic61—41no—
234C2×Dic61C4×D411yescharacteristic
235C2×Dic61C22×D411yescharacteristic
236C2×Dic61C2×#4111yescharacteristic
237D244—21no—
238D244—21no—
239C4×D61—21no—
240C4×D61—21no—
241C4×D61—21no—
242C4×D61—21no—
243C4×D61—41no—
244C4×D61—41no—
245C4×D61—41no—
246C4×D61—81no—
247C4×D61—81no—
248Dic122—42no—
249#92420—21no—
250#92420—21no—
251#92420—21no—
252#92420—21no—
253#92420—41no—
254#92420—41no—
255#92420—41no—
256#92420—41no—
257#92420—41no—
258#92420—41no—
259C8×C61—21no—
260C8×C61—21no—
261#92418—21no—
262#92418—21no—
263#18028—611nomaximal, Sylow
264C22×C61—22no—
265C22×C61—41no—
266C22×C61—41no—
267C22×C61C2×C4×D411yescharacteristic
268C2×D61—21no—
269C2×D61—21no—
270C2×D61—21no—
271C2×D61—41no—
272C2×D61—41no—
273C2×D61—41no—
274C2×D61—84no—
275C4×C61—21no—
276C4×C61—21no—
277C4×C61—41no—
278C4×C61—41no—
279C4×C61—41no—
280C4×C61C2×#13111yescharacteristic
281C4×C61#56811yescharacteristic
282Dic61—21no—
283Dic61—21no—
284Dic61—41no—
285Dic61—41no—
286Dic61—41no—
287Dic61#57711yescharacteristic
288Dic61#57711yescharacteristic
289#3101—611no—
290#2986—611no—
291#2974—611no—
292#1592—611no—
293#1590—611no—
294#1588—611no—
295#1585—611no—
296#1583—611no—
297#1582—611no—
298SD16⋊C8—611no—
299C8×SD16—611no—
300#1572—611no—
301#1497—611no—
302#1478—611no—
303#1454—611no—
304C2×C61—42no—
305C2×C61#293311yescharacteristic
306C2×C61#294911yescharacteristic
307C2×C61#295511yescharacteristic
308D61—41no—
309D61—81no—
310#533—611no—
311C2×C4×D4—611no—
312#483—611no—
313#483—611no—
314#476—611no—
315#476—611no—
316#461—611no—
317#461#692311yescharacteristic
318#450—611no—
319#450—611no—
320#446—611no—
321#446—611no—
322#446—1221no—
323C8×Q8—611no—
324C8×Q8—611no—
325C8×Q8—1221no—
326C4×SD16—611no—
327C4×SD16—611no—
328C4×SD16—611no—
329C4×SD16—611no—
330#436—611no—
331#436—611no—
332#435—1221no—
333#435—1221no—
334C8×D4—611no—
335C8×D4—611no—
336#433—1221no—
337#433—1221no—
338#432—611no—
339#431—611no—
340#431—611no—
341#431—611no—
342#431—611no—
343#407—1221no—
344C2×C22⋊C8—1221no—
345#335—611no—
346#335—611no—
347#334—611no—
348#334—611no—
349Q8⋊C8—611no—
350Q8⋊C8—611no—
351Q8⋊C8—611no—
352Q8⋊C8—611no—
353D4⋊C8—611no—
354D4⋊C8—611no—
355D4⋊C8—611no—
356D4⋊C8—611no—
357#322—611no—
358#322—611no—
359#322—611no—
360C82—611no—
361C61#1802811yescharacteristic, complemented, Sylow
362C22×D4—611no—
363C23×C4—1221no—
364C2×SD16—611no—
365C2×SD16—611no—
366C2×SD16C2×#692311yescharacteristic
367C2×SD16C2×#692311yescharacteristic
368C2×M16—1221no—
369C2×M16—1221no—
370C22×C8—1221no—
371C22×C8—1221no—
372C4⋊Q8—611no—
373C4⋊Q8C2×#692311yescharacteristic
374#125—1221no—
375C22⋊Q8—611no—
376C22⋊Q8—611no—
377C22⋊Q8—1221no—
378C4×Q8—611no—
379C4×Q8—611no—
380C4×Q8—1221no—
381C4×D4—611no—
382C4×D4—611no—
383C4×D4—611no—
384C4×D4—1221no—
385C4×D4—1221no—
386C4×D4C2×#692311yescharacteristic
387#117—1221no—
388C2×C4⋊C4—611no—
389C2×C22⋊C4—1221no—
390C2×C42—611no—
391#106—611no—
392#106—611no—
393#106—611no—
394#106—611no—
395C4⋊C8—611no—
396C4⋊C8—611no—
397C4⋊C8—611no—
398C4⋊C8—611no—
399C4⋊C8—611no—
400C4⋊C8—611no—
401C4⋊C8—611no—
402C4⋊C8—1221no—
403C4⋊C8—1221no—
404C4⋊C8—1221no—
405C4⋊C8—1221no—
406C4⋊C8—1221no—
407C4⋊C8C2×#692311yescharacteristic
408#103—611no—
409#103—611no—
410#103C2×#692311yescharacteristic
411#103C2×#692311yescharacteristic
412#102—611no—
413#102—611no—
414#102—611no—
415#102—611no—
416C22⋊C8—611no—
417C22⋊C8—611no—
418C22⋊C8—611no—
419C22⋊C8—611no—
420C22⋊C8—1221no—
421C22⋊C8—1221no—
422C22⋊C8—1221no—
423C22⋊C8—1221no—
424C22⋊C8—1221no—
425C22⋊C8—1221no—
426C22⋊C8—1221no—
427#97—1221no—
428#97—1221no—
429#97—1221no—
430C4×C8—611no—
431C4×C8—611no—
432C4×C8—611no—
433C4×C8—611no—
434C4×C8—611no—
435C4×C8—611no—
436C4×C8—1221no—
437C4×C8—1221no—
438C4×C8—1221no—
439C24—1221no—
440C2×Q8—1221no—
441C2×Q8C22×#692311yescharacteristic
442C2×Q8C22×#692311yescharacteristic
443C2×D4—611no—
444C2×D4—1221no—
445C2×D4—1222no—
446C2×D4—2441no—
447C2×D4C22×#692311yescharacteristic
448C22×C4—21no—
449C22×C4—611no—
450C22×C4—611no—
451C22×C4—611no—
452C22×C4—1221no—
453C22×C4—1221no—
454C22×C4—1221no—
455C22×C4—1221no—
456C22×C4—4881no—
457C22×C4—4881no—
458SD16—22no—
459SD16—22no—
460SD16—2441no—
461SD16—2441no—
462M16—4881no—
463M16—4881no—
464C2×C8—611no—
465C2×C8—611no—
466C2×C8—611no—
467C2×C8—611no—
468C2×C8—611no—
469C2×C8—611no—
470C2×C8—1221no—
471C2×C8—1221no—
472C2×C8—1221no—
473C2×C8—1221no—
474C2×C8—1221no—
475C2×C8—1221no—
476C2×C8—4881no—
477C2×C8—4881no—
478C2×C8C22×#692311yescharacteristic
479C2×C8C22×#692311yescharacteristic
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—611no—
483C4⋊C4—611no—
484C4⋊C4—611no—
485C4⋊C4—1221no—
486C4⋊C4—1221no—
487C4⋊C4—1221no—
488C4⋊C4—1221no—
489C4⋊C4—1221no—
490C4⋊C4—1221no—
491C4⋊C4C22×#692311yescharacteristic
492C22⋊C4—21no—
493C22⋊C4—1221no—
494C22⋊C4—1221no—
495C22⋊C4—1221no—
496C22⋊C4—1221no—
497C22⋊C4—1221no—
498C42—611no—
499C42—611no—
500C42—611no—
501C42—1221no—
502C42—1221no—
503C42C22×#692311yescharacteristic
504C23—21no—
505C23—611no—
506C23—1221no—
507C23—4881no—
508C23—2442no—
509C23—2442no—
510Q8—21no—
511Q8—21no—
512Q8—21no—
513Q8—21no—
514Q8—2442no—
515D4—21no—
516D4—1221no—
517D4—1221no—
518D4—2442no—
519D4#1451986412yes—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—81no—
524C2×C4—611no—
525C2×C4—611no—
526C2×C4—611no—
527C2×C4—1221no—
528C2×C4—1221no—
529C2×C4—1221no—
530C2×C4—1221no—
531C2×C4—1221no—
532C2×C4—1221no—
533C2×C4—1221no—
534C2×C4—4881no—
535C2×C4—4881no—
536C2×C4—2441no—
537C2×C4—2441no—
538C2×C4—2441no—
539C2×C4—2441no—
540C2×C4—2441no—
541C2×C4D4×#692311yescharacteristic
542C2×C4D4×#692311yescharacteristic
543C2×C4C23×#692311yescharacteristic
544C8—21no—
545C8—21no—
546C8—1221no—
547C8—1221no—
548C8—1221no—
549C8—1221no—
550C8—1221no—
551C8—1221no—
552C8—2441no—
553C8—2441no—
554C8—2441no—
555C8—2441no—
556C8—2441no—
557C8—2441no—
558C22—22no—
559C22—41no—
560C22—41no—
561C22—1221no—
562C22—1221no—
563C22—1221no—
564C22—4884no—
565C22—2441no—
566C22—2441no—
567C22—2441no—
568C22C2×D4×#692311yescharacteristic
569C4—21no—
570C4—21no—
571C4—41no—
572C4—41no—
573C4—41no—
574C4—611no—
575C4—611no—
576C4—1221no—
577C4—1221no—
578C4—2441no—
579C4—2441no—
580C4—2441no—
581C4C2×#1451986411yescharacteristic
582C4#1684084111yescharacteristic
583C2—42no—
584C2—4881no—
585C2—2441no—
586C2#2146254911yescharacteristic
587C2#2146257911yescharacteristic
588C2#2146259211yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#461C4
socleC22×C61C2×C4×D4
prime radicalC2×D4×D61C2×C4
cosocleC4×Dic61C24
hypercenter#461#6923
hypocenterC61#18028
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #461

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #21462730C2semidirect
3. #21461463C2semidirect
4. #21461453C2semidirect
5. #21461446C2semidirect
6. #21461436C2semidirect
7. #21461426C2semidirect
8. #21461424C2semidirect
9. SD16⋊#92420C2semidirect
10. SD16×#92420C2semidirect
11. #21461391C2semidirect
12. #21461182C2semidirect
14. #21461041C2semidirect
16. #16840813C22semidirect
17. #16840813C22semidirect
20. Q8×#92420C22semidirect
21. Q8×#92420C22semidirect
36. #16840626C22semidirect
37. #16840625C22semidirect
38. #16840624C22semidirect
39. #16840623C22semidirect
40. Q8⋊#92420C22semidirect
41. Q8⋊#92420C22semidirect
42. Q8⋊#92420C22semidirect
43. Q8⋊#92420C22semidirect
48. #92420⋊C8C22semidirect
49. #92420⋊C8C22semidirect
50. #16840603C22semidirect
51. C8×#92420C22semidirect
361. C61#18028semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#214627302
#214626792
#214614632
#214614532
#214614462
#214614362
#214614262
#214614242
SD16⋊#924202
SD16×#924202
#214613912
#214611822
#214611192
#214610412
#214558262
#1802861